Without either a beginningfinished goods inventory or an ending finished goods inventory what formula would I use to provide those pieces of data

There isn't a specific formula, because in real life we aren't missing those numbers. So it depends on what information you have been given. For instance, do you have cost of goods manufactured, good solds? Are you sure there's a beginning inventory. (i.e. maybe a new company?)

There are four numbers that would run through that account: beginning inventory, adding cost of goods manufactured, subtracting cost of goods sold, and then ending inventory. You can't solve for two variables unless there's no beginning inventory, or you've got some other good information to get you to one of those numbers. I have no idea what type of information you have.